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How to change symbolic expressions containing a relational operator

I have expressions containing a relational operator, symbols, and constants. I would like to rearrange the expressions so that (as much as possible) all the constant members are on one side of the relational operator, and the other members are on the other. For example, I would like to change:

x - 5> y - z

at

x - y + z> 5

Is there an existing sympy method for this? If not, where should I start with the sympy extension?

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2 answers

, " ". , (LHS) , .

, . . (RHS) . , - / .

:

import sympy
from sympy.core.relational import Relational

mult_by_minus_one_map = {
    None: '==',
    '==': '==',
    'eq': '==',
    '!=': '!=',
    '<>': '!=',
    'ne': '!=',
    '>=': '<=',
    'ge': '<=',
    '<=': '>=',
    'le': '>=',
    '>': '<',
    'gt': '<',
    '<': '>',
    'lt': '>',
}

def move_inequality_constants(ineq, zero_on_right=False):
    l = ineq.lhs
    r = ineq.rhs
    op = ineq.rel_op
    all_on_left = l - r
    if zero_on_right:
        return Relational(all_on_left, sympy.sympify(0), op)
    else:
        coeff_dict = all_on_left.as_coefficients_dict()
        var_types = coeff_dict.keys()
        new_rhs = sympy.sympify(0)
        for s in var_types:
            if s == 1:
                all_on_left = all_on_left - coeff_dict[s]
                new_rhs = new_rhs - coeff_dict[s]
        if new_rhs < 0:
            all_on_left = all_on_left * -1
            new_rhs = new_rhs * -1
            op = mult_by_minus_one_map[op]
        return Relational(all_on_left,new_rhs,op)

# test code to demo function below    
from sympy.abc import x,y,z

test_ineqs = [ x - 5 > y - z,
               x**2 + x - 5 > y + x**2 - z,
               x + 5 > y - z,
               x**3 + y**2 >= x + 5*y - z - 15]

for k in test_ineqs:
    print('Re-arranging '+ str(k))
    kn = move_inequality_constants(k)
    print('Gives '+str(kn))
    print('Or equivalently ' + str(move_inequality_constants(k, True)))
    print('====')

:

Re-arranging x - 5 > y - z
Gives x - y + z > 5
Or equivalently x - y + z - 5 > 0
====
Re-arranging x**2 + x - 5 > x**2 + y - z
Gives x - y + z > 5
Or equivalently x - y + z - 5 > 0
====
Re-arranging x + 5 > y - z
Gives -x + y - z < 5
Or equivalently x - y + z + 5 > 0
====
Re-arranging x**3 + y**2 >= x + 5*y - z - 15
Gives -x**3 + x - y**2 + 5*y - z <= 15
Or equivalently x**3 - x + y**2 - 5*y + z + 15 >= 0
+1

canonical, , .

, else :

r, l = (ineq.lhs - ineq.rhs).as_coeff_Add()
if r < 0:
    l, r = -r, -l
return Relational(l, r, ineq.rel_op).canonical

, , 2x<4y x<2*y. SymPy , .

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